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SUMMARY:New equations for inextensible sheets with applications to Moebius
  strips and helical nanoribbons - Gert Van der Heijden (University College
  London)
DTSTART:20080502T140000Z
DTEND:20080502T150000Z
UID:TALK11523@talks.cam.ac.uk
CONTACT:Nami Norman
DESCRIPTION:We derive a new set of geometrically-exact equilibrium equatio
 ns for the\ndeformation of thin inextensible strips of finite width. The e
 quations are\nthe Euler-Lagrange equations for a geometrical variational p
 roblem with a\nfunctional in terms of the curvature and torsion of the str
 ip's axial curve\nas well as their derivatives with respect to arclength. 
 The equations are\nused to solve the long-standing problem of finding the 
 characteristic shape\nof a material Moebius strip. Solutions for increasin
 g width-to-length ratio\nshow the formation of creases bounding nearly fla
 t triangular regions\, a\nfeature also familiar from fabric draping and pa
 per crumpling. This suggests\nthat our approach could give new insight int
 o energy localisation phenomena\nin unstretchable elastic sheets\, which f
 or instance could help to predict\npoints of onset of tearing.\n   The tec
 hnique for deriving equilibrium equations can be generalised to\nintrinsic
 ally curved sheets (shells). In the second part of the talk we\nwill apply
  this to study the force-extension behaviour of helical ribbons.\nA comple
 te analytical study of stretched/compressed exact helical solutions\ncan b
 e carried out. Unlike previous rod models our strip model predicts\nhyster
 esis behaviour for low-pitch ribbons of arbitrary material properties.\nAs
 sociated with it is a first-order transition between two different helical
 \nstates\, a phenomenon observed in experiments with cholesterol ribbons.\
 nNumerical solutions for non-helical solutions reveal a new non-uniform\nu
 ncoiling scenario in which a ribbon of very low pitch shears under tension
 \nand successively releases a sequence of almost planar loops. Our results
  may\nbe relevant for nanoscale devices such as force probes.\n\n
LOCATION:Engineering Department - LR6
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